Heuristics and Algorithms for Roots of Non-Linear Equations
Chaman L. Sabharwal · International Journal of Latest Engineering and Management Research (IJLEMR) · 2023
Optimization problems lead to solving non-linear equations for calculating the value of a parameter, that is the root of the equation.Numerical iterative techniques are frequently used to find roots of an equation when analytic solution is not available.Nascent hybrid techniques to find roots of an equation is new to the fundamental problem in diverse fields.Recently, there have been some attempts to design hybrid algorithms for efficient solutions.Here we strive for a new hybrid algorithm which is an intuitive approach to hybridization.In this paper, we design and implement two new algorithms: (1) a new Quadsection algorithm extending the Trisection algorithm, (2) a hybrid algorithm, Hybrid 4, that is more efficient than the existing hybrid algorithms.Hybrid 4 algorithm is a blend of Quadsection algorithm and Regula Falsi algorithm.The implementation results validate that the new algorithm, Hybrid4, surpasses the efficiency of existing hybrid algorithms Hybrid 1, Hybrid 2, and Hybrid 3 algorithms.This paper contributes an essential hybrid algorithm to the repertoire of hybrid root finding algorithms.